This text covers all aspects of terrestrial and celestial coordinate reference systems and frames in geodesy, from historical geodetic datums to modern international reference systems and the transformations between them. The exposition is divided into two parts, terrestrial and the celestial reference systems, where the focus of the latter is primarily in the transformation to the former. The geometry of the ellipsoid is covered in detail, as well as astronomic coordinates and astrogeodetic methods. The new reference system conventions recently (2003) adopted by the International Astronomical Union (IAU) and the International Earth Rotation and Reference Systems Service (IERS) are included, but are presented as a supplement to the classic transformation between the celestial and terrestrial systems. The adjective, geometric, in the title implies that no attempt is made to introduce the Earth’s gravity field, which historically (more so than today) formed such an integral part of geodetic control. Vertical control today is largely achieved geometrically with GPS, and therefore, the vertical datum (still important for many applications) is covered only in passing, relegating it to other more appropriate venues (such as a study of Earth’s gravity field). The text concludes with a comprehensive discussion of time (the fourth dimension), which is also treated as a reference system.